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arXiv · 1507.08253

Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes

Cheng Cheng·Sylvain Crovisier·Shaobo Gan·Xiaodong Wang·Dawei Yang
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Abstract

We prove that, for $C^1$-generic diffeomorphisms, if a homoclinic class is not hyperbolic, then there is a non-hyperbolic ergodic measure supported on it. This proves a conjecture by Díaz and Gorodetski [28]. We also discuss the conjectured existence of periodic points with different stable dimension in the class.

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Cheng Cheng, Sylvain Crovisier, Shaobo Gan, Xiaodong Wang, Dawei Yang. 2015-07-29. Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes. https://arxiv.org/abs/1507.08253

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